Differential Version Research Articles

Planckian corrections to the Friedmann flat equations from thermodynamics at the apparent horizon

In this paper, we use our recently generalized black hole entropy formula to propose a quantum version of the Friedmann equations. In particular, starting from the differential version of the first law of thermodynamics, we are able to find Planckian (noncommutative) corrections to the Friedmann flat equations. The so modified equations are formally similar to the ones present in Gauss–Bonnet gravity, but in the ordinary 3+1 dimensions. As a consequence of these corrections, by considering negative fluctuations in the internal energy that are allowed by quantum field theory, our equations imply a maximum value both for the energy density [Formula: see text] and for the Hubble flow H, i.e. the big bang is ruled out. Conversely, by considering positive quantum fluctuations, we found no maximum for [Formula: see text] and H. Nevertheless, by starting with an early time energy density [Formula: see text], we obtain a value for the scale factor [Formula: see text], implying a finite Planckian universe at t = 0, i.e. the point-like big bang singularity is substituted by a universe of Planckian size at t = 0. Finally, we found possible higher order Planckian terms to our equations together with the related corrections of our generalized Bekenstein–Hawking entropy.

Of Miles and Oscillators: Reflections on Miles A. Copeland

When I started writing this article, I realized that I have never watched Miles Copeland give a lecture to a class or a technical presentation at a conference. Also, I never experienced Miles as a graduate student supervisor or as a professor. On the contrary, this article is about the Miles I know best?Miles the consultant, the engineer, the friend for over 21 years. During most of those years, especially in his retirement, Miles has been meticulously investigating the large signal and phase noise operation and design of the Colpitts oscillator whose differential IC version he introduced for the first time with his graduate student Leonard Dauphinee at the IEEE International Solid-State Circuits Conference (ISSCC) in 1997 [1]. Copeland and Colpitts are a perfect fit. Few people are aware, and I am sure that not even Miles knew at the time, that although universally known as an American scientist and engineer, Edwin Colpitts was born, raised, educated, and buried in New Brunswick, Canada.

Superstability and central extensions of algebraic groups

Altinel and Cherlin proved that any perfect central extension of a simple algebraic group over an algebraically closed field which happens to be of finite Morley rank is actually a finite central extension and is itself an algebraic group. We will prove an infinite rank version of their result with an additional hypothesis, while giving an example which shows the necessity of this hypothesis. The inspiration for the work comes from differential algebra; namely, a differential algebraic version of the results here was used by the second author to answer a question of Cassidy and Singer. The work here also provides an alternate path to the same answer.An almost simple superstable group G is one in which every definable normal subgroup H has the property that RU(G)>RU(H)⋅n for any n∈N. We prove that any almost simple superstable group which is a central extension of a simple algebraic group is actually a finite central extension and is an algebraic group. We also explain the applications of this result to differential algebraic groups. Many of the central ideas of the proof of our main theorem are an adaptation of techniques developed by the second author in the setting of differential algebraic groups.

Bayesian Planet Searches for the 10 cm/s Radial Velocity Era

AbstractA new apodized Keplerian model is proposed for the analysis of precision radial velocity (RV) data to model both planetary and stellar activity (SA) induced RV signals. A symmetrical Gaussian apodization function with unknown width and center can distinguish planetary signals from SA signals on the basis of the width of the apodization function. The general model for m apodized Keplerian signals also includes a linear regression term between RV and the stellar activity diagnostic In (R'hk), as well as an extra Gaussian noise term with unknown standard deviation. The model parameters are explored using a Bayesian fusion MCMC code. A differential version of the Generalized Lomb-Scargle periodogram provides an additional way of distinguishing SA signals and helps guide the choice of new periods. Sample results are reported for a recent international RV blind challenge which included multiple state of the art simulated data sets supported by a variety of stellar activity diagnostics.

Modifying the pom-pom model for extensional viscosity overshoots

We have developed a variant of the pom-pom model that qualitatively describes two surprising features recently observed in filament stretching rheometer experiments of uniaxial extensional flow of industrial branched polymer resins: (i) Overshoots of the transient stress during steady flow and (ii) strongly accelerated stress relaxation upon cessation of the flow beyond the overshoot. Within the context of our model, these overshoots originate from entanglement stripping (ES) during the processes of normal chain retraction and branch point withdrawal. We demonstrate that, for a single mode, the predictions of our overshoot model are qualitatively consistent with experimental data. To provide a quantitative fit, we represent an industrial melt by a superposition of several individual modes. We show that a minimal version of our model, in which ES due to normal chain retraction is omitted, can provide a reasonable, but not perfect, fit to the data. With regard the stress relaxation after (kinematically) steady flow, we demonstrate that the differential version of tube orientation dynamics in the original pom-pom model performs anomalously. We discuss the reasons for this and suggest a suitable alternative.

A differential version of the Chebyshev–Markov–Stieltjes inequalities

We show that a differential version of the classical Chebyshev–Markov–Stieltjes inequalities holds for a broad family of weight functions. Such a differential version appears to be new. Our results apply to weight functions which are bounded away from zero and piecewise absolutely continuous and yield effective estimates when the weight satisfies additional regularity conditions.

Sharp existence criteria for positive solutions of Hardy--Sobolev type systems

This paper examines systems of poly-harmonic equations of the Hardy--Sobolev type and the closely related weighted systems of integral equations involving Riesz potentials. Namely, it is shown that the two systems are equivalent under some appropriate conditions. Then a sharp criterion for the existence and non-existence of positive solutions is determined for both differential and integral versions of a Hardy--Sobolev type system with variable coefficients. In the constant coefficient case, Liouville type theorems for positive radial solutions are also established using radial decay estimates and Pohozaev type identities in integral form.

Straightforward Approximate Stochastic Equilibria for Nonlinear Rational Expectations Models

We present a new approach to the approximation of equilibrium solutions to nonlinear rational expectations models that applies to any order of approximation. The approach relies on a particular version of Taylor series approximations -- the differential version -- and on a scalar perturbation of the support of the entire history of shocks. The resulting solution for any order can always be directly cast in a linear state-space form, permitting the solution to be used for many practical applications such as forecasting, estimation, and computing impulse responses. Using the approach, we show that there cannot be multiple solutions in any order of approximation if the associated first-order approximate solution is determinate. Our approach can be used simply to verify key propositions of the earlier literature, to extend its range of applications, and to resolve puzzles left by it. While the paper only provides an explicit solution up to a third-order approximation, extensions to any higher order approximations are straightforward.

Sumset and Inverse Sumset Inequalities for Differential Entropy and Mutual Information

The sumset and inverse sumset theories of Freiman, Pl\"{u}nnecke and Ruzsa, give bounds connecting the cardinality of the sumset $A+B=\{a+b\;;\;a\in A,\,b\in B\}$ of two discrete sets $A,B$, to the cardinalities (or the finer structure) of the original sets $A,B$. For example, the sum-difference bound of Ruzsa states that, $|A+B|\,|A|\,|B|\leq|A-B|^3$, where the difference set $A-B= \{a-b\;;\;a\in A,\,b\in B\}$. Interpreting the differential entropy $h(X)$ of a continuous random variable $X$ as (the logarithm of) the size of the effective support of $X$, the main contribution of this paper is a series of natural information-theoretic analogs for these results. For example, the Ruzsa sum-difference bound becomes the new inequality, $h(X+Y)+h(X)+h(Y)\leq 3h(X-Y)$, for any pair of independent continuous random variables $X$ and $Y$. Our results include differential-entropy versions of Ruzsa's triangle inequality, the Pl\"{u}nnecke-Ruzsa inequality, and the Balog-Szemer\'{e}di-Gowers lemma. Also we give a differential entropy version of the Freiman-Green-Ruzsa inverse-sumset theorem, which can be seen as a quantitative converse to the entropy power inequality. Versions of most of these results for the discrete entropy $H(X)$ were recently proved by Tao, relying heavily on a strong, functional form of the submodularity property of $H(X)$. Since differential entropy is {\em not} functionally submodular, in the continuous case many of the corresponding discrete proofs fail, in many cases requiring substantially new proof strategies. We find that the basic property that naturally replaces the discrete functional submodularity, is the data processing property of mutual information.

Theoretical semi-empirical study of the glycine molecule interaction with fullerene [C.sub.60

Modeling of the quantum interaction properties of glycine radicals on the fullerene C 60 are investigated by MINDO/3 (Modified Intermediate Neglect of Differential Overlap version 3) calculations. It is found that the interaction potential of the C-centered glycine radical with the fullerene C 60 lead to a stable complexes when it reacts with the carbon atom (C 1 -centered) and metastable conformations with N atoms. We have studied the effect of two rotations (θ and φ) characteristics of the fullerene C 60 on binding the amino acid. Our results suggest that the binding energy is lower as the glycine rotate increases, and as the carboxyl group rotate increases. Also the stability (binding energy) fluctuate decreases.

Fine properties of [formula omitted]-cocycles which allow abundance of simple and trivial spectrum

In this paper we prove that the class of accessible and saddle-conservative cocycles (a wide class which includes cocycles evolving in GL(d,R), SL(d,R) and Sp(d,R)) Lp-densely have a simple spectrum. We also prove that for an Lp-residual subset of accessible cocycles we have a one-point spectrum. Finally, we show that the linear differential system versions of previous results also hold and give some applications.

Vibrational Resonance in a Duffing System with a Generalized Delayed Feedback

We investigate the vibrational resonance in the Duffing system with different kinds of delayed feedback. Our approach is to consider the delayed feedback as a generalized delayed feedback in a fractional-order differential version. For three special cases, the generalized delayed feedback corresponds to displacement delayed feedback, velocity delayed feedback, and acceleration delayed feedback respectively. At first, based on the vibrational mechanism, the approximate solution of the system is obtained. Then, we give conditions for all resonance patterns. The the oretical predictions are verified by numerical simulations. Furthermore, the theoretical results are in good agreement with the numerical simulations. Since the delayed feedback is in a generalized form, our results can be regarded as universal for the vibrational resonance in nonlinear systems with different kinds of delayed feedback.

Psychometric properties of the Hungarian version of Differentiation of Self Inventory (DSI-H)

Psychometric properties of the Hungarian version of Differentiation of Self Inventory (DSI-H)

Validation of the Chinese version of Differentiation of Self Inventory (C-DSI).

Although the need to develop objective assessment tools in different cultures is well-recognized, there is a severe lack of objective measures about emotional functioning in the Chinese context. This project conducted three studies to validate the Chinese version of the Differentiation of Self Inventory (DSI). Study 1 looked at the factor structure, internal consistency, concurrent validity, and construct validity of the C-DSI. Study 2 examined the test-retest reliability of the C-DSI. Study 3 tested the discriminant validity of the C-DSI in a clinical sample and in a nonclinical sample and examined its correlations with the General Contentment Scale (GCS). The study results suggested that the C-DSI possesses good psychometric properties. Findings also indicated implications of divergent cultures and hinted at treatment implications--taking the familistic orientation and the Chinese meaning of self into consideration to understand the differentiation of self in the Chinese culture context.

Comparison Between Reduced Basis and Stochastic Collocation Methods for Elliptic Problems

The stochastic collocation method (Babuska et al. in SIAM J Numer Anal 45(3):1005---1034, 2007; Nobile et al. in SIAM J Numer Anal 46(5):2411---2442, 2008a; SIAM J Numer Anal 46(5):2309---2345, 2008b; Xiu and Hesthaven in SIAM J Sci Comput 27(3):1118---1139, 2005) has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method (Maday et al. in Comptes Rendus Mathematique 335(3):289---294, 2002; Patera and Rozza in Reduced basis approximation and a posteriori error estimation for parametrized partial differential equations Version 1.0. Copyright MIT, http://augustine.mit.edu , 2007; Rozza et al. in Arch Comput Methods Eng 15(3):229---275, 2008), primarily developed for solving parametric systems, has been recently used to deal with stochastic problems (Boyaval et al. in Comput Methods Appl Mech Eng 198(41---44):3187---3206, 2009; Arch Comput Methods Eng 17:435---454, 2010). In this work, we aim at comparing the performance of the two methods when applied to the solution of linear stochastic elliptic problems. Two important comparison criteria are considered: (1), convergence results of the approximation error; (2), computational costs for both offline construction and online evaluation. Numerical experiments are performed for problems from low dimensions $$O(1)$$ O ( 1 ) to moderate dimensions $$O(10)$$ O ( 10 ) and to high dimensions $$O(100)$$ O ( 100 ) . The main result stemming from our comparison is that the reduced basis method converges better in theory and faster in practice than the stochastic collocation method for smooth problems, and is more suitable for large scale and high dimensional stochastic problems when considering computational costs.

A nullstellensatz and a positivstellensatz for ordered differential fields

AbstractWe use the model completeness and axiomatisation of the theory of closed ordered differential fields to give a differential version of Dubois, Krivine and Risler's nullstellensatz and Stengle's positivstellensatz for ordered fields.

Differential Landauer's principle

Landauer's principle states that the erasure of information must be a dissipative process. In this paper, we carefully analyze the recording and erasure of information on a physical memory. On the one hand, we show that, in order to record some information, the memory has to be driven out of equilibrium. On the other hand, we derive a differential version of Landauer's principle: We link the rate at which entropy is produced at every time of the erasure process to the rate at which information is erased.

A Noniterative Method for Locating Soft Faults in Complex Wire Networks

Reflectometry-based methods are the standard choice for fault-detection techniques in wire networks. While effective when dealing with simple networks and relatively hard faults, their results can be of more difficult interpretation if a network presents more than two branches. In this paper, we propose the use of an alternative technique based on a coherent multiport characterization of a network under test. The data thus collected are used to define excitation signals that will be focusing over the position of a fault, following a method already successfully applied in geophysical prospection techniques and nondestructive testing, namely, the DORT method, based on the synthesis of time-reversed signals. It is shown that a direct transposition of this technique to wire networks is not possible, due to the guided nature of wave propagation in wire networks, leading to the impossibility of assuming a dominant direction of propagation, as opposed to the case of propagation in open media. A differential version of the DORT method is introduced, enabling an accurate identification of the original position of faults. Numerical and experimental results are presented to demonstrate the feasibility of this approach.

A new method to enhance frequency operation of CMOS ring oscillators

This article proposes a frequency-boosting method for CMOS ring oscillators. It consists of adding RC-based differentiators in delay cells to speed up their transient responses. Two novel delay cells for simple and differential versions are presented. On using MOS transistor components to implement the differentiators, the resulting increase of surface area is observed to be moderate, and this allows frequency tuning by voltage control, without inducing additional phase noise. The presented circuits are suitable for low-voltage operation. Simulation results on the proposed circuits have shown significant frequency enhancement with a competitive factor of merit.

Low-voltage differential voltage follower for WTA and fully differential applications

A low-voltage differential version of a high performance voltage follower is presented. The proposed circuit is very compact, and symmetric with respect to the input devices. Both differential input devices are enhanced by local shunt feedback, increasing the gain and, thus, reducing the output resistance for higher precision. The circuit has proved useful as a winner-take-all (WTA) circuit. It also features operation as a fully differential amplifier with low supply voltage requirements close to a transistor's threshold voltage. Experimental results verifying the operation of the proposed structure are provided.